Extremes of Periodic Integer-Valued Sequences with Exponential Type Tails

Abstract

This paper aims to analyze the extremal properties of periodic integer-valued sequences with marginal distribution belonging to a particular class defined by Anderson [1970. J. Appl. Probab. 7, 99–113] where the tail decays exponentially. An expression for calculating the extremal index of sequences satisfying certain local conditions, similar to those introduced by Chernick et al. [1991. Adv. Appl. Prob. 6, 711–731] is obtained. An application to infinite moving averages and max-autoregressive sequences is included. These results generalize the ones obtained for the stationary case.